Question 664·Easy·Algebra

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\begin{cases} 2x + y = 13 \\ y = 7 \end{cases}

What is the solution $(x, y)$ to the system of equations above?

A system of equations asks for one ordered pair that makes both equations true. If an equation already gives you one variable, use it to fix that coordinate. Then graph both equations as written in Desmos and click their intersection to find the other coordinate. Keep the order straight: $x$ comes first, then $y$ .

Hints

Hint 1
A solution to a system must work in both equations. One equation already gives $y$ , so you know the second coordinate of $(x,y)$ . What does the pair look like before you find $x$ ?
Hint 2
The intersection is the point where two graphs meet, so it satisfies both equations. Type each equation as written in Desmos and click where the lines cross. Read the first coordinate to find $x$ .

Step-by-step

Approach 1: Read the intersection in Desmos
Step 1
Fix the second coordinate
A system asks for a pair that makes both equations true. Since $y=7$ , the second coordinate of $(x,y)$ is $7$ , so the solution must look like $(x,7)$ .
Step 2
Find the shared point
Type $2x+y=13$ and $y=7$ on separate Desmos lines, then click their intersection, where the lines meet. Desmos shows $(3,7)$ . The first coordinate is $x$ , so the solution to the system is $(3,7)$ . Choice D.

Approach 2: Substitute the known value
Step 1
Replace $y$ with $7$
Because $y$ and $7$ are equal, substitution lets you put $7$ in place of $y$ in the first equation:
$2x+7=13.$
Now the equation has only $x$ left to find.
Step 2
Isolate the $x$ term
Subtract $7$ from both sides:
$2x=6.$
The $2$ still multiplies $x$ , so $6$ isn't the value of $x$ yet.
Step 3
Complete the ordered pair
Divide both sides by $2$ :
$x=3.$
The ordered pair puts $x$ before $y$ , so with $y=7$ , the solution is $(3,7)$ . Choice D.

Question 664·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

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